ETA: Wikipedia has reminded me the feature was called UniversalXPConnect, and it was a Firefox thing and wasn't cross-browser. It still sucks that it was removed without sensible replacement.
TiddlySaver.jar was one such workaround. A check in the Wayback Machine suggests that it was originally required only for Safari, Opera, and Chrome; IE and Firefox needed no such plugin. Nowadays, there are several workarounds, and setting up one is a mandatory installation step: standalone applications, browser extensions, servers, etc. Some are clunky (e.g. you have to keep your wiki in your Downloads directory or the browser can't write to it), and either way, TiddlyWiki is no longer truly a single stand-alone HTML file, at least not for writing purposes. It's still a very versatile tool, though.